The cost C of printing a newspaper is partly constant and partly varies as n the number of printed newspapers. If the cost of printing 500 newspapers is $320 and the cost of printing 1000newpapers is $540, find the total cost of printing 750 newspapers
Let C1 be the constant cost of printing and C2 be the cost that varies with the number of newspapers.
From the given information, we have:
C1 + C2(500) = 320 (1)
C1 + C2(1000) = 540 (2)
Subtracting equation (1) from equation (2), we get:
C2(1000) - C2(500) = 540 - 320
C2(500) = 220
Dividing both sides by 500, we get:
C2 = 220/500
C2 = 0.44
Now, substitute the value of C2 in equation (1) to find C1:
C1 + 0.44(500) = 320
C1 + 220 = 320
C1 = 320 - 220
C1 = 100
Therefore, the total cost of printing 750 newspapers is:
C = C1 + C2(n)
C = 100 + 0.44(750)
C = 100 + 330
C = $430. Answer: \boxed{430}.
To find the total cost of printing 750 newspapers, we need to determine the constant cost and the variable cost component.
Let's assume the constant cost is represented by C1 and the variable cost per newspaper is represented by C2.
We are given two data points:
- When printing 500 newspapers, the cost is $320.
- When printing 1000 newspapers, the cost is $540.
Using this information, we can set up a system of equations to solve for C1 and C2.
Equation 1: C1 + 500C2 = 320
Equation 2: C1 + 1000C2 = 540
To solve the system of equations, we can use the substitution method or elimination method.
Let's use the elimination method to solve the system of equations:
Multiply Equation 1 by -2:
-2(C1 + 500C2) = -2(320)
-2C1 - 1000C2 = -640
Now, add this equation to Equation 2:
-2C1 - 1000C2 + C1 + 1000C2 = -640 + 540
-C1 = -100
Divide both sides by -1:
C1 = 100
Now substitute the value of C1 into Equation 1:
100 + 500C2 = 320
Subtract 100 from both sides:
500C2 = 220
Divide both sides by 500:
C2 = 220/500
C2 = 0.44
So, the variable cost per newspaper is $0.44, and the constant cost is $100.
To find the total cost of printing 750 newspapers, we can use the formula:
Total cost = Constant cost + Variable cost per newspaper * Number of newspapers
Total cost = $100 + $0.44 * 750
Total cost = $100 + $330
Total cost = $430
Therefore, the total cost of printing 750 newspapers is $430.
To solve this problem, you need to first identify the constant and variable components of the cost C.
Given that the cost of printing 500 newspapers is $320 and the cost of printing 1000 newspapers is $540, we can use this information to determine the constant cost component and the variable cost component.
Let's assign variables to the constant and variable components:
- Constant cost = a
- Variable cost per newspaper = b
Now we can set up the following equations:
For the cost of printing 500 newspapers:
C = a + 500b
320 = a + 500b (Equation 1)
For the cost of printing 1000 newspapers:
C = a + 1000b
540 = a + 1000b (Equation 2)
To find the values of a and b, we need to solve this system of equations.
Subtract Equation 1 from Equation 2:
540 - 320 = (a + 1000b) - (a + 500b)
220 = 500b
b = 220/500
b = 0.44
Now we can substitute the value of b back into Equation 1 to find the value of a:
320 = a + 500(0.44)
320 = a + 220
a = 320 - 220
a = 100
Now that we know the values of a and b, we can find the total cost C for printing 750 newspapers:
C = a + 750b
C = 100 + 750(0.44)
C = 100 + 330
C = 430
Therefore, the total cost of printing 750 newspapers is $430.